Problem: Simplify the following expression: $ a = \dfrac{5x - 9}{9} + \dfrac{-5}{7} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{5x - 9}{9} \times \dfrac{7}{7} = \dfrac{35x - 63}{63} $ Multiply the second expression by $\dfrac{9}{9}$ $ \dfrac{-5}{7} \times \dfrac{9}{9} = \dfrac{-45}{63} $ Therefore $ a = \dfrac{35x - 63}{63} + \dfrac{-45}{63} $ Now the expressions have the same denominator we can simply add the numerators: $a = \dfrac{35x - 63 - 45}{63} $ $a = \dfrac{35x - 108}{63}$